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单词 InferenceRule
释义

inference rule


In logic, an inference rule is a rule whereby one may correctlydraw a conclusionMathworldPlanetmath from one or more premises. For example, the law ofthe contrapositive allows one to conclude a statement of the form

¬Q¬P

from a premise of the form

PQ.

Here, ‘P’ and ‘Q’ are propositional variables, which can stand forarbitrary propositionsPlanetmathPlanetmathPlanetmath. A popular way to indicate applications of rulesof inference is to list the premises above a line and write theconclusions below the line. For instance, we might indicate the lawof the contrapositive thus:

PQ¬Q¬P

A typical application of the law ofcontrapositive would be to conclude ”If my clothes are dry, then it is notraining”, from ”If it rains, then my clothes will be wet.” which could beexpressed as follows using the notation described above:

If it rains, then my clothes will be wet.If my clothes are dry, then it is not raining.

(In thisinstance, P is “It is raining” and Q is “My clothes are dry”.

An important feature of rules of inference is that they are purely formal,which means that all that matters is the form of the expression;meaning is not a consideration in applying a rule of inference.Thus, the following are equally valid applications of the rule ofthe contrapositive:

If the jabberwocky is mimsy, then the toves blithe.If the toves are not blithing, then the jabberwocky is not mimsy.
If my cat has a tail, then my cat is a dog.If my cat is not a dog, then my cat does not have a tail.

In the first example, the statements are nonsense and in the secondexample, the statements are false, but this doesn’t matter — bothexamples constitute valid apllications of the rule of the contrapositive.Of course, in order to draw valid conclusions, we need to start withvalid premises, but the point of these examples is clarify thedistinction between valid statements and valid applications ofrules of inference.

Titleinference rule
Canonical nameInferenceRule
Date of creation2013-03-22 16:50:51
Last modified on2013-03-22 16:50:51
Ownerrspuzio (6075)
Last modified byrspuzio (6075)
Numerical id8
Authorrspuzio (6075)
Entry typeDefinition
Classificationmsc 03B35
Classificationmsc 03B22
Classificationmsc 03B05
Synonymrule of inference
Related topicModusPonens
Related topicLogicalAxiom
Related topicDeductiveSystem
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更新时间:2025/5/4 20:14:27